232k views
2 votes
How do I do this? can I get a step by step so I understand well.

How do I do this? can I get a step by step so I understand well.-example-1
User Dmorlock
by
7.8k points

1 Answer

3 votes

general geometric formula is


A_n=A_1\cdot r^(n-1)

then we replace using A3


\begin{gathered} A_3=A_1\cdot r^(3-1) \\ \\ (16)/(3)=A_1\cdot r^2 \end{gathered}

now replace using A5


\begin{gathered} A_5=A_1\cdot r^(5-1) \\ \\ (64)/(21)=A_1\cdot r^4 \end{gathered}

now we have two equations and two unknow


\begin{gathered} (16)/(3)=A_1\cdot r^2 \\ \\ (64)/(21)=A_1\cdot r^4 \end{gathered}

we can solve A1 or r from any equation and replace on the other

I will solve A1 from the first equation


A_1=((16)/(3))/(r^2)

and replace on the second to solve r


\begin{gathered} (64)/(21)=(((16)/(3))/(r^2))\cdot r^4 \\ \\ (64)/(21)=(16)/(3)\cdot r^2 \\ \\ r^2=(64*3)/(21*16) \\ \\ r^2=(192)/(336)=(4)/(7) \\ \\ r=\frac{2\sqrt[]{7}}{7} \end{gathered}

now replace r on the other equation to find A1


\begin{gathered} (16)/(3)=A_1\cdot(\frac{2\sqrt[]{7}}{7})^2 \\ \\ (16)/(3)=A_1\cdot(4)/(7) \\ \\ A_1=(16*7)/(4*3) \\ \\ A_1=(28)/(3) \end{gathered}

now we have the two unknows A1 and r then replace on the general geometric equation


A_n=(28)/(3)\cdot(\frac{2\sqrt[]{7}}{7})^(n-1)

User Nima Rostami
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories